Our work continues in a line of recent work for constructing confidence sets for more general classes of
differentially private estimators.
[1]} shows how to combine estimates from additive functions that respect zCDP to get confidence intervals
at no additional cost.
[2]} provides confidence intervals for models trained with objective or
output perturbation algorithms. These algorithms are quite general, but require
solving the non-private ERM sub-problem optimally.
[3]} presents a very general approach based on privately estimating parameters of the
data-generating distribution and bootstrapping confidence intervals by
repeatedly running the model of interest on samples from a distribution parameterized by the privately estimated parameters.
This method is efficient with respect to its use of the privacy budget, but relies on significant knowledge of
the structure of the data-generating process.
With the exception of [4]}, these works largely ignore the issue of bounding \(\mathcal {X}\)  effectively
and the ramifications of this not being done appropriately.
